Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte

Autores:: Castellanos González, Miguel Armando
Peña Garzón, Laura Givelly

Tipo de recurso:: Article of journal

Fecha de publicación:: 2026

Institución:: Universidad Pedagógica y Tecnológica de Colombia

Repositorio:: RiUPTC: Repositorio Institucional UPTC

Idioma:: spa

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dc.title.es-ES.fl_str_mv	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
title	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
spellingShingle	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte Cálculo mental Procesos cognitivos Educación matemática Sentido numérico Memoria de trabajo Revisión documental.
title_short	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
title_full	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
title_fullStr	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
title_full_unstemmed	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
title_sort	Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte
dc.creator.fl_str_mv	Castellanos González, Miguel Armando Peña Garzón, Laura Givelly
dc.contributor.author.spa.fl_str_mv	Castellanos González, Miguel Armando Peña Garzón, Laura Givelly
dc.subject.none.fl_str_mv	Cálculo mental Procesos cognitivos Educación matemática Sentido numérico Memoria de trabajo Revisión documental.
topic	Cálculo mental Procesos cognitivos Educación matemática Sentido numérico Memoria de trabajo Revisión documental.
publishDate	2026
dc.date.accessioned.none.fl_str_mv	2026-04-21 16:10:52
dc.date.available.none.fl_str_mv	2026-04-21 16:10:52
dc.date.issued.none.fl_str_mv	2026-04-21
dc.type.spa.fl_str_mv	Artículo de revista
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dc.relation.references.spa.fl_str_mv	Agostini, F., Zoccolotti, P., & Casagrande, M. (2022). Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature. Brain Sciences, 12(2), 239. https://doi.org/10.3390/brainsci12020239 Anghileri, J. (2006). Teaching number sense (2.ª ed.). Continuum. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1–2), 75–106. https://doi.org/10.1016/0010-0277(92)90051-I Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417-423. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. En G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 8, pp. 47-89). Academic Press. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. En A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1-33). Erlbaum. Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24(4), 294-323. Butterworth, B. (2010). Foundational Numerical Capacities and the Origins of Dyscalculia. Trends in Cognitive Sciences, 14(12), 534–541. Cowan, R., & Lamb, R. (2021). Numerical development from kindergarten to third grade. Cognitive Development, 59, 101067. De Smedt, B. (2022). Cognitive neuroscience of mathematical learning and development. Nature Reviews Psychology, 1(2), 95–108. https://doi.org/10.1038/s44159-021-00008-5 DeStefano, D., & LeFevre, J. A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353-386. Dowker, A. (2005). Individual Differences in Arithmetic. Psychology Press. Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., & Hamlett, C. L. (2016). Pathways to Third-Grade Calculation versus Word-Reading Competence. Developmental Psychology, 52(3). Gilmore, C. (2023). Understanding the complexities of mathematical cognition: A multi-level framework. Quarterly Journal of Experimental Psychology, 76(9), 1953–1972. https://doi.org/10.1177/17470218231175325 Geary, D. C. (2011). Cognitive Predictors of Achievement Growth in Mathematics. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510 Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170–218. Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. Journal of Mathematical Behavior, 23(4), 443-463. Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96(4), 284–309. https://doi.org/10.1016/j.jecp.2006.09.001 Ji, Z., & Guo, K. (2023). The association between working memory and mathematical problem solving: A three-level meta-analysis. Frontiers in Psychology, 14, 1091126. Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early Math Matters. Learning and Individual Differences, 19(1), 82–92. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental Dyscalculia and Basic Numerical Capacities. Cognition, 93(2), 99–125. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory & Cognition, 22(4), 395-410. Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired Acuity of the Approximate Number System Underlies Mathematical Learning Disability. Child Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-44. Medrano, J., & Prather, R. W. (2023). Rethinking executive functions in mathematical cognition. Journal of Cognition and Development, 24(2), 280–295. https://doi.org/10.1080/15248372.2023.2172414 Mononen, R., & Niemivirta, M. (2023). Patterns of symbolic numerical magnitude processing and working memory as predictors of early mathematics performance. European Journal of Psychology of Education, 38(1), 311–332. https://doi.org/10.1007/s10212-021-00596-4 Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., & Carraher, J. (2007). The Contribution of Logical Reasoning to the Learning of Mathematics. British Journal of Educational Psychology, 77(3), 625–650. Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348-367. Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. Reys, R., Reys, B., Nohda, N., & Emori, H. (1995). Mental computation performance and strategy use of Japanese students in grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26(4), 304-326. Reys, R., Reys, B., Emanuelsson, G., Johansson, B., McIntosh, A., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics. En C. Donlan (Ed.), The development of mathematical skills (pp. 75-110). Psychology Press. Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372 Skagenholt, M., Skagerlund, K., & Träff, U. (2025). Numerical cognition across the lifespan: A selective review of key developmental stages and neural, cognitive, and affective underpinnings. Cortex, 184, 263–286. https://doi.org/10.1016/j.cortex.2025.01.005 Sowder, J. T. (1990). Mental computation and number sense. Arithmetic Teacher, 37(7), 18-20. Starkey, P., & Cooper, R. G., Jr. (1980). Perception of numbers by human infants. Science, 210(4473), 1033–1035. https://doi.org/10.1126/science.7434028 Thompson, I., & Bramald, R. (2002). An investigation of the relationship between young children's understanding of the concept of place value and their competence at mental addition. University of Newcastle upon Tyne. Threlfall, J. (2002). Flexible mental calculation. Educational Studies in Mathematics, 50(1), 29-47. Threlfall, J. (2009). Strategies and flexibility in mental calculation. ZDM, 41(5), 541-555. Vanbinst, K., & De Smedt, B. (2016). Individual differences in children's mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. Progress in Brain Research, 227, 105–130. https://doi.org/10.1016/bs.pbr.2016.04.001 Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3-14. Vogel, S. E., & De Smedt, B. (2021). Developmental brain mechanisms of numerical and arithmetic processing. Developmental Review, 60, 100964. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749-750. Yang, D. C. (2002). Teaching and learning number sense: One successful process-oriented activity with sixth grade students in Taiwan. School Science and Mathematics, 102(4), 152-157. Yang, D. C. (2005). Number sense strategies used by 6th-grade students in Taiwan. Educational Studies, 31(3), 317-334.
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spelling	Castellanos González, Miguel ArmandoPeña Garzón, Laura Givelly2026-04-21 16:10:522026-04-21 16:10:522026-04-212215-8391https://repositorio.uptc.edu.co/handle/001/2244210.19053/uptc.22158391.214412745-2166https://doi.org/10.19053/uptc.22158391.21441application/pdfspaUptcRevista Habitus: Semilleros de investigación - 2026https://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessEsta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.http://purl.org/coar/access_right/c_abf2https://revistas.uptc.edu.co/index.php/semilleros_investigacion/article/view/21441Cálculo mentalProcesos cognitivosEducación matemáticaSentido numéricoMemoria de trabajoRevisión documental.Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del ArteArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/articleJournal articleinfo:eu-repo/semantics/publishedVersionTexthttp://purl.org/coar/version/c_970fb48d4fbd8a85Agostini, F., Zoccolotti, P., & Casagrande, M. (2022). Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature. Brain Sciences, 12(2), 239. https://doi.org/10.3390/brainsci12020239 Anghileri, J. (2006). Teaching number sense (2.ª ed.). Continuum. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1–2), 75–106. https://doi.org/10.1016/0010-0277(92)90051-I Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417-423. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. En G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 8, pp. 47-89). Academic Press. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. En A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1-33). Erlbaum. Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24(4), 294-323. Butterworth, B. (2010). Foundational Numerical Capacities and the Origins of Dyscalculia. Trends in Cognitive Sciences, 14(12), 534–541. Cowan, R., & Lamb, R. (2021). Numerical development from kindergarten to third grade. Cognitive Development, 59, 101067. De Smedt, B. (2022). Cognitive neuroscience of mathematical learning and development. Nature Reviews Psychology, 1(2), 95–108. https://doi.org/10.1038/s44159-021-00008-5 DeStefano, D., & LeFevre, J. A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353-386. Dowker, A. (2005). Individual Differences in Arithmetic. Psychology Press. Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., & Hamlett, C. L. (2016). Pathways to Third-Grade Calculation versus Word-Reading Competence. Developmental Psychology, 52(3). Gilmore, C. (2023). Understanding the complexities of mathematical cognition: A multi-level framework. Quarterly Journal of Experimental Psychology, 76(9), 1953–1972. https://doi.org/10.1177/17470218231175325 Geary, D. C. (2011). Cognitive Predictors of Achievement Growth in Mathematics. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510 Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170–218. Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. Journal of Mathematical Behavior, 23(4), 443-463. Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96(4), 284–309. https://doi.org/10.1016/j.jecp.2006.09.001 Ji, Z., & Guo, K. (2023). The association between working memory and mathematical problem solving: A three-level meta-analysis. Frontiers in Psychology, 14, 1091126. Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early Math Matters. Learning and Individual Differences, 19(1), 82–92. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental Dyscalculia and Basic Numerical Capacities. Cognition, 93(2), 99–125. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory & Cognition, 22(4), 395-410. Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired Acuity of the Approximate Number System Underlies Mathematical Learning Disability. Child Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-44. Medrano, J., & Prather, R. W. (2023). Rethinking executive functions in mathematical cognition. Journal of Cognition and Development, 24(2), 280–295. https://doi.org/10.1080/15248372.2023.2172414 Mononen, R., & Niemivirta, M. (2023). Patterns of symbolic numerical magnitude processing and working memory as predictors of early mathematics performance. European Journal of Psychology of Education, 38(1), 311–332. https://doi.org/10.1007/s10212-021-00596-4 Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., & Carraher, J. (2007). The Contribution of Logical Reasoning to the Learning of Mathematics. British Journal of Educational Psychology, 77(3), 625–650. Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348-367. Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. Reys, R., Reys, B., Nohda, N., & Emori, H. (1995). Mental computation performance and strategy use of Japanese students in grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26(4), 304-326. Reys, R., Reys, B., Emanuelsson, G., Johansson, B., McIntosh, A., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics. En C. Donlan (Ed.), The development of mathematical skills (pp. 75-110). Psychology Press. Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372 Skagenholt, M., Skagerlund, K., & Träff, U. (2025). Numerical cognition across the lifespan: A selective review of key developmental stages and neural, cognitive, and affective underpinnings. Cortex, 184, 263–286. https://doi.org/10.1016/j.cortex.2025.01.005 Sowder, J. T. (1990). Mental computation and number sense. Arithmetic Teacher, 37(7), 18-20. Starkey, P., & Cooper, R. G., Jr. (1980). Perception of numbers by human infants. Science, 210(4473), 1033–1035. https://doi.org/10.1126/science.7434028 Thompson, I., & Bramald, R. (2002). An investigation of the relationship between young children's understanding of the concept of place value and their competence at mental addition. University of Newcastle upon Tyne. Threlfall, J. (2002). Flexible mental calculation. Educational Studies in Mathematics, 50(1), 29-47. Threlfall, J. (2009). Strategies and flexibility in mental calculation. ZDM, 41(5), 541-555. Vanbinst, K., & De Smedt, B. (2016). Individual differences in children's mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. Progress in Brain Research, 227, 105–130. https://doi.org/10.1016/bs.pbr.2016.04.001 Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3-14. Vogel, S. E., & De Smedt, B. (2021). Developmental brain mechanisms of numerical and arithmetic processing. Developmental Review, 60, 100964. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749-750. Yang, D. C. (2002). Teaching and learning number sense: One successful process-oriented activity with sixth grade students in Taiwan. School Science and Mathematics, 102(4), 152-157. Yang, D. C. (2005). Number sense strategies used by 6th-grade students in Taiwan. Educational Studies, 31(3), 317-334.96Revista Habitus: Semilleros de investigaciónhttps://revistas.uptc.edu.co/index.php/semilleros_investigacion/article/download/21441/17240PublicationOREORE.xmltext/xml2617https://repositorio.uptc.edu.co/bitstreams/e3278113-b823-4b8f-82ed-1991281610b4/download8449eaa5053911a604b44aaa5c8fc4ddMD51falseAnonymousREAD001/22442oai:repositorio.uptc.edu.co:001/224422026-10-29 13:59:58.177https://creativecommons.org/licenses/by-nc-nd/4.0metadata.onlyhttps://repositorio.uptc.edu.coRepositorio Institucional UPTCbdigital@metabiblioteca.com

Cálculo mental como Proceso Cognitivo: Una Revisión teórica del estado del Arte

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